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Logic Gates
Logic Gates
 A logic gate is an elementary building block of a
digital circuit .
 Most logic gates have two inputs and one output.
 At any given moment, every terminal is in one of the
two binary conditions low (0) or high (1), represented
by different voltage levels.
Boolean Constants and Variables
 Boolean 0 and 1 do not represent actual numbers but
instead represent the state, or logic level.
Logic 0
False
Off
Low
No
Open switch
Logic 1
True
On
High
Yes
Closed switch
Three Basic Logic Operations
 OR
 AND
 NOT
 Other derived logic operations
 NOR
 NAND
 XOR
 XNOR
Truth Tables
 A truth table is a means for describing how a logic
circuit’s output depends on the logic levels present at
the circuit’s inputs.
Inputs
A
0
0
1
1
B
0
1
0
1
Output
x
1
0
1
0
A
?
B
x
OR Gate
 The OR gate gets its name from the fact that it
behaves after the fashion of the logical inclusive "or."
 The output is "true" if either or both of the inputs are
"true."
 If both inputs are "false," then the output is "false."
OR Operation
 Boolean expression for the OR operation:
x =A + B
 The above expression is read as “x equals A OR B”
OR Gate
 An OR gate is a gate that has two or more inputs and
whose output is equal to the OR combination of the
inputs.
The switch equivalent of an
OR gate
AND Gate
 The AND gate is so named because, if 0 is called
"false" and 1 is called "true,"
 the gate acts in the same way as the logical "and"
operator.
AND Operation
 Boolean expression for the AND operation:
x =A B
 The above expression is read as “x equals A AND B”
AND Gate
 An AND gate is a gate that has two or more inputs and
whose output is equal to the AND product of the
inputs.
The switch equivalent of an
AND gate
NOT Operation
 A logical inverter , sometimes called a NOT gate to
differentiate it from other types of electronic inverter
devices,
 has only one input.
 It reverses the logic state.
NOT
 BooleanOperation
expression for the NOT operation:
x= A
 The above expression is read as “x equals the inverse of A”
 Also known as inversion or complementation.
 Can also be expressed as: A’
A
The switch equivalent of a
NOT gate
NOR gate
 The NOR gate is a combination OR gate followed by
an inverter.
 Its output is "true" if both inputs are "false.“
 Otherwise, the output is "false."
NOR Gate
 Boolean expression for the NOR operation:
x=A+B
The NAND gate
 The NAND gate operates as an AND gate followed by a
NOT gate.
 It acts in the manner of the logical operation "and"
followed by negation.
 The output is "false" if both inputs are "true.“
 Otherwise, the output is "true."
NAND Gate
 Boolean expression for the NAND operation:
x=AB
alternative symbol for NOR
function
XOR ( exclusive-OR ) gate
 The XOR ( exclusive-OR ) gate acts in the same way as
the logical "either/or."
 The output is "true" if either, but not both, of the
inputs are "true."
 The output is "false" if both inputs are "false" or if
both inputs are "true."
XOR ( exclusive-OR ) gate
 Another way of looking at this circuit is to observe
that the output is 1 if the inputs are different, but 0 if
the inputs are the same.
XOR gate
XOR ( exclusive-OR ) gate
Input 1
Input 2
Output
0
0
0
0
1
1
1
0
1
1
1
0
XNOR (exclusive-NOR) gate
 The XNOR (exclusive-NOR) gate is a combination
XOR gate followed by an inverter.
 Its output is "true" if the inputs are the same,
and"false" if the inputs are different
XNOR gate
XNOR (exclusive-NOR) gate
Input 1
Input 2
Output
0
0
1
0
1
0
1
0
0
1
1
1
Describing Logic Circuits
Algebraically
 Any logic circuits can be built from the three basic




building blocks: OR, AND, NOT
Example 1: x = A B + C
Example 2: x = (A+B)C
Example 3: x = (A+B)
Example 4: x = ABC (A+D)
Examples 1,2
Examples 3
Example 4
Evaluating Logic Circuit Output
 Evaluation rule for Boolean expression
1) Perform all inversions of single terms
2) Perform all operations within parentheses
3) Perform an AND operation before an OR operation
4) If an expression has a bar over it, perform the expression first
and then invert the result
Evaluating Logic-Circuit
Outputs
 x = ABC(A+D)
 Determine the output x given A=0, B=1, C=1, D=1.
 Can also determine output level from a diagram
Implementing Circuits from
Boolean Expressions
 y = AC+BC’+A’BC
 x=(A+B)(B’+C)
y = AC+BC’+A’BC
x=(A+B)(B’+C)
Alternate Logic Symbols
 Sometimes the logic of a circuit is more easily
understood if an alternative gate shape is used.
 DeMorgan=s Theorem can be used to determine
equivalent logic gates.
Alternate Logic Symbols
 Rules:
 1. Change the gate shape (AND ==> OR; OR ==>
AND).
 2. Change the bubbles (add where missing; remove if
present).
Alternate Logic-Gate
Representation